Power Flow Studies Using MATLAB

Power Flow Studies Using MATLAB

Executive Summary

The report aims to show the differences between Newton-Raphson and Gauss-Seidel methods by using them to analyse a power flow system. During the study in a two-bus system, with a slack bus and PQ bus, two convergence tolerances were used. The case study 1 compares the iterative process of the two methods for a voltage tolerance convergence and case study 2 compares the iterative process of the two methods for a power mismatch convergence. The main points that investigated are the results and the speed of convergence. Although, both methods converge to the same values, Newton-Raphson converges exponentially and compared to Gauss-Seidel which converges linearly, needs only around half iterations to return the expected result.

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Table of Contents

Executive Summary

Introduction

Background Theory

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Newton-Raphson Method

Gauss-Seidel Method

Power Flow Study Results and Analysis

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Case Study 1

Case Study 2

Analysis of the results and convergence characteristics acquired by the Newton-Raphson and Gauss-Seidel methods

Conclusions

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References

Introduction

A load or power flow analysis is a computational procedure required to determine the sinusoidal steady state of the entire power system. The mathematical solution includes a system of nonlinear algebraic equations, which during an iterative process, the values converge to only one solution. The outcome of the power flow analysis is the acquisition of the voltage magnitudes and angles at each bus. Once the voltage magnitudes and angles at each bus have been acquired using power flow analysis, the real and reactive power at each branch of the power system can be computed. Furthermore, losses in particular lines can be computed by investigating the difference between the power flow in the sending and receiving ends and by determining over and under load conditions, the appropriate solution is taken into consideration. In the power industry, load flow analysis is used on a daily basis as it is essential in determining the fault-free, stable and economical operation of existing power systems, as well as for future expansion of power systems.

A two-bus system is given in Figure 1 below.